Your hips are closed almost all the time, making it harder for you to balance.. It looks like you're leaning forward all the time and never 'sitting'.

You'll have better balance and engage your glutes and quads more easily if you just learn to get your upper legs and hips to open up.. you're hitting with your hips always closed and I can see it making things harder than they have to be, especially on your backhand side.

quick edit: look at where your kneecaps are pointing relative to each other most of the time.. they're facing inward, or 'buckling' too often. Pro players' kneecaps will be at an obtuse angle to each other after their split step, and in their power step before hitting. Practice a horse stance like in kung fu movies! Put some weight on your butt!